3u^2=12u-6

Solution for 3u^2=12u-6 equation:

Simplifying
3u2 = 12u + -6

Reorder the terms:
3u2 = -6 + 12u

Solving
3u2 = -6 + 12u

Solving for variable 'u'.

Reorder the terms:
6 + -12u + 3u2 = -6 + 12u + 6 + -12u

Reorder the terms:
6 + -12u + 3u2 = -6 + 6 + 12u + -12u

Combine like terms: -6 + 6 = 0
6 + -12u + 3u2 = 0 + 12u + -12u
6 + -12u + 3u2 = 12u + -12u

Combine like terms: 12u + -12u = 0
6 + -12u + 3u2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -4u + u2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -4u + u2)' equal to zero and attempt to solve:

Simplifying
2 + -4u + u2 = 0

Solving
2 + -4u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4u + -2 + u2 = 0 + -2

Reorder the terms:
2 + -2 + -4u + u2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4u + u2 = 0 + -2
-4u + u2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4u + u2 = -2

The u term is -4u.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4u + 4 + u2 = -2 + 4

Reorder the terms:
4 + -4u + u2 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + -4u + u2 = 2

Factor a perfect square on the left side:
(u + -2)(u + -2) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(u + -2) equal to 1.414213562 and -1.414213562.

Subproblem 1
u + -2 = 1.414213562

Simplifying
u + -2 = 1.414213562

Reorder the terms:
-2 + u = 1.414213562

Solving
-2 + u = 1.414213562

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + u = 1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + u = 1.414213562 + 2
u = 1.414213562 + 2

Combine like terms: 1.414213562 + 2 = 3.414213562
u = 3.414213562

Simplifying
u = 3.414213562

Subproblem 2
u + -2 = -1.414213562

Simplifying
u + -2 = -1.414213562

Reorder the terms:
-2 + u = -1.414213562

Solving
-2 + u = -1.414213562

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + u = -1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + u = -1.414213562 + 2
u = -1.414213562 + 2

Combine like terms: -1.414213562 + 2 = 0.585786438
u = 0.585786438

Simplifying
u = 0.585786438

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {3.414213562, 0.585786438}
Solution
u = {3.414213562, 0.585786438}